All three will undergo physiotherapy treatment, with Atletico unable to put a time frame on their respective recoveries.
“An MRI scan was carried out on Moya on Thursday after the injury he suffered in training last Wednesday,” Atleti said in a statement.
“The medical results show that our goalkeeper has suffered a muscle injury in the femoral biceps of the left thigh. He will face physiotherapy and rehabilitation treatment.
“Argentine midfielder Nico Gaitan is suffering from arthritis in the metatarsophalangeal joint of the first toe of his left foot. As with Moya, he will undergo physiotherapy treatment and rehabilitation.
“Finally, Kevin Gameiro felt discomfort after the friendly match played in Paris between the national teams of France and Spain. Our striker has undergone an MRI scan that confirms that he is suffering from tendinitis in the adductor of his left thigh.
“He will also be put in the hands of our physios in order to return as soon as possible.”
The news will be most unwelcome for head coach Diego Simeone, with Atleti facing a tough fixture schedule over the next two weeks.
LaLiga matches against Malaga and Real Sociedad precede a derby meeting with Real Madrid at the Santiago Bernabeu on April 8, before the Champions League quarter-final first leg against Leicester City four days later.